Numerical Investigation on Evolution of Tip Vortices Generated by Low-Aspect Ratio Rectangular Wings at High Angle of Attack

  • Jae Hoon Lee
  • Yong Oun HanEmail author
Original Paper


The onset and evolution of tip vortices generated by the vertical tip of a straight half wing, with a NACA 0012 airfoil section, were studied at a Reynolds number of 1 × 105 by a steady-state calculation at high angles of attack, namely, 10°, 18°, and 42°, where the maximum lift, deep stall, and second peak of the lift coefficient occur, respectively, with three different aspect ratios: 2, 3, and 4. It was found that the counter-rotating vortex wrap initiated within the short wake period at higher angles than the deep stall and affected the contraction of the core trail, as well as resulting in the calculated swirl velocity component exhibiting a significant deviation from the conventional model fit. It was noted that the swirl strength of tip vortices increased continuously, even up to the deep stall phase, where the lift started to decrease immediately after the first peak. Wake contraction was found to follow an exponential decay in the earlier wake region. Compared to both the infinite wing and the elliptical wing, the finite square wing seems to have an offset in the lift coefficient, which could represent the tip loss.


High angle of attack Tip vortex Aspect ratio Numerical investigation Vatistas modified model 



This work was supported by the 2014 year Yeungnam University Research Grant.


  1. 1.
    Critzos CC, Heyson HH, Boswinkle RW Jr (1955) Aerodynamic characteristics of NACA0012 airfoil section at angle of attack from 0 to 180 degrees. NACA TN3361Google Scholar
  2. 2.
    Sheldahl RE, Klimas PC (1981) Aerodynamic characteristics of seven symmetrical airfoil sections through 180-degree angle of attack for use in aerodynamic analysis of vertical axis aerodynamic analysis of vertical axis wind turbines, SAND-80-2114. Sandia National Laboratories Energy Report.
  3. 3.
    Spera DA (2008) Models of lift and drag coefficients of stalled and unstalled airfoils in wind turbines and wind tunnels, NASA/CR-2008-215434Google Scholar
  4. 4.
    Lind AH, Lefebvre JN, Jones AR (2014) Time-averaged aerodynamics of sharp and blunt trailing-edge static airfoils in reverse flow. AIAA 52(12):2751–2764. CrossRefGoogle Scholar
  5. 5.
    Park BH, Han YO (2018) Steady aerodynamic and flow behaviors of two-dimensional NACA0012 airfoil in one revolution angle of attack. IJASS 19(1):pp. CrossRefGoogle Scholar
  6. 6.
    Prandtl L (1921) Applications of modern hydrodynamics to aeronautics, NACA Report No. 116Google Scholar
  7. 7.
    Corsiglia VR, Schwind RG, Chigier NA (1973) Rapid scanning, three-dimensional hot-wire anemometer surveys of wing-tip vortices. J Aircr 10(12):752–757. CrossRefGoogle Scholar
  8. 8.
    Dacles-Mariani J, Zilliac GG, Chow JS, Bradshaw P (1995) Numerical/experimental study of a wingtip vortex in the near field. AIAA J 33(9):1561–1568. CrossRefGoogle Scholar
  9. 9.
    Ghias R, Mittal R, Dong H, Lund T (2005) Study of tip-vortex formation using large-eddy simulation, In: 43rd AIAA aerospace sciences meeting and exhibit, p 1280.
  10. 10.
    Spalart PR, Allmaras SR (1992) A one-equation turbulence model for aerodynamic flows. In: 30th aerospace sciences meeting and exhibit, p 439.
  11. 11.
    ANSYS Fluent Theory Guide (2013) release15.0, ANSYS IncGoogle Scholar
  12. 12.
    Ahsan M (2014) Numerical analysis of friction factor for a fully developed turbulent flow using k–ε turbulence model with enhanced wall treatment. Beni-Suef Univ J Basic Appl Sci 3(4):269–277. CrossRefGoogle Scholar
  13. 13.
    Polhamus EC (1969) A concept of the vortex lift of the vortex lift of sharp edge delta wings based on a leading edge suction analogy, NASA Technical note, NASA-TN-D-3767Google Scholar
  14. 14.
    Hsiao CT, Pauley LL (1998) Numerical study of the steady-state tip vortex flow over a finite-span hydrofoil. J Fluids Eng 120:345–353. CrossRefGoogle Scholar
  15. 15.
    Spentzos A, Barakos GN, Badcock KJ, Richards BE, Wernert P, Schreck S, Raffel M (2005) Investigation of three-dimensional dynamic stall using computational fluid dynamics. AIAA J 43(5):1023–1033. CrossRefGoogle Scholar
  16. 16.
    Tairo K, Colonius T (2009) Three-dimensional flows around low-aspect ratio flat plate wings at low Reynolds numbers. JFM 623:187–207. CrossRefzbMATHGoogle Scholar
  17. 17.
    Anande GK, Sukumar PP, Selig MS (2015) Measured aerodynamic characteristics of wings at low Reynolds numbers. Aerosp Sci Technol 42:392–406. CrossRefGoogle Scholar
  18. 18.
    Gerz T, Holzäpfel F, Darracq D (2002) Commercial aircraft wake vortices. Prog Aerosp Sci 38(3):181–208. CrossRefGoogle Scholar
  19. 19.
    Han YO, Leishman G (2004) Investigation of helicopter rotor blade tip vortex alleviation using a slotted tip. AIAA J 42(3):524–535. CrossRefGoogle Scholar
  20. 20.
    You JY, Kwon OJ, Han YO (2009) Viscous flow simulation of rotor blades with tip slots in hover. J Am Helicopter Soc 54(1):012006–1–012006-9. CrossRefGoogle Scholar
  21. 21.
    Lamb H (1932) Hydrodynamics. Cambridge University Press, New York, pp 592–593, 668–669Google Scholar
  22. 22.
    Vatistas GH, Kozel V, Mih WC (1991) Simpler model for concentrated vortices. Exp Fluids 24(11):73–76. CrossRefGoogle Scholar
  23. 23.
    Milne-Thompson LM (1968) Theoretical hydrodynamics, 5th edn. Macmillan & Co., Ltd., London, p 355CrossRefGoogle Scholar
  24. 24.
    Vatistas GH (2006) Simple model for turbulent tip vortices. J Aircr 43(5):1577–1579. CrossRefGoogle Scholar
  25. 25.
    Devenport WJ, Rife MC, Liapis SI, Follin GJ (1996) The structure and development of a wing tip vortex. J Fluid Mech 312:67–106. MathSciNetCrossRefGoogle Scholar
  26. 26.
    Birch D, Lee T, Mokhtarian F, Kafyeke F (1992) Rollup and near-field behavior of a tip vortex. J Aircr 40(3):603–607. CrossRefGoogle Scholar
  27. 27.
    Bailey SCC, Tavoularis S, Lee BHK (2006) Effects of free-stream turbulence on wing-tip vortex formation and near field. J Aircr 43(5):1282–1291. CrossRefGoogle Scholar
  28. 28.
    Chang JW, Park SO (2000) Measurements in the tip vortex roll-up region of an oscillating wing. AIAA J 38(6):1092–1095. CrossRefGoogle Scholar
  29. 29.
    Tung C, Pucci SL, Caradonna FX, Morse HA (1981) The structure of trailing vortices generated by model rotor blades, NASA Technical MemorandumGoogle Scholar
  30. 30.
    Han YO, Leishman G, Coyne AJ (1997) Measurements of the velocity and turbulence structure of a rotor tip vortex. AIAA J 35(3):477–485. CrossRefGoogle Scholar
  31. 31.
    Landgrebe AJ (1972) The wake geometry of a hovering helicopter rotor and its influence on rotor performance. J Helicopter Soc 17(4):2–15. CrossRefGoogle Scholar

Copyright information

© The Korean Society for Aeronautical & Space Sciences and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringYeungnam UniversityGyeongsanRepublic of Korea

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